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If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the
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13 Apr 2018, 06:13
13 Apr 2018, 06:13
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If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following must be true?
A. ab < 0
B. ab > 0
C. a - b > 0
D. a + b < 0
E. a + b > 0
A. ab < 0
B. ab > 0
C. a - b > 0
D. a + b < 0
E. a + b > 0
Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the
[#permalink]
16 Apr 2018, 20:58
16 Apr 2018, 20:58
1
Let \(a = -1\)
Let \(b = -2\)
Then \(|a| + |b| = 1 + 2 =3\)
and, \(|a + b| = |-3|= 3\)
Similarly,
Let \(a = 1\)
Let \(b = 2\)
Then, \(|a| + |b| = 1 + 2 =3\)
and, \(|a + b| = |3|= 3\)
Therefore either \(a,b\) can be \(-1,-2\) or \(1,2\)
The correct option should satisfy both the condition for \((a,b)\)
only option b does that since \(a*b\) is always\(+\)ve since we are multiplying \(2\) \(+\)ve numbers or 2 \(-\)ve numbers which will always be \(+\)ve.
Let \(b = -2\)
Then \(|a| + |b| = 1 + 2 =3\)
and, \(|a + b| = |-3|= 3\)
Similarly,
Let \(a = 1\)
Let \(b = 2\)
Then, \(|a| + |b| = 1 + 2 =3\)
and, \(|a + b| = |3|= 3\)
Therefore either \(a,b\) can be \(-1,-2\) or \(1,2\)
The correct option should satisfy both the condition for \((a,b)\)
only option b does that since \(a*b\) is always\(+\)ve since we are multiplying \(2\) \(+\)ve numbers or 2 \(-\)ve numbers which will always be \(+\)ve.
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Re: If |a| + |b| = |a + b|, a 0, and b 0, then which of the
[#permalink]
09 Dec 2023, 03:16
09 Dec 2023, 03:16
Theory : |a| + |b| = |a + b| when both a and b have the same sign
=> Either both a and b are positive or both a and b are negative (or both are zero which is not the case here)
=> ab > 0 (as ab>0 also means the same thing. Either both a and b are positive or both are negative)
Watch this video to Master Inequalities!
So, Answer will be B
Hope it helps!
Watch the following video to MASTER Absolute Values
=> Either both a and b are positive or both a and b are negative (or both are zero which is not the case here)
=> ab > 0 (as ab>0 also means the same thing. Either both a and b are positive or both are negative)
Watch this video to Master Inequalities!
So, Answer will be B
Hope it helps!
Watch the following video to MASTER Absolute Values
